Topic
Coproduct
About: Coproduct is a research topic. Over the lifetime, 162 publications have been published within this topic receiving 1510 citations. The topic is also known as: categorical sum.
Papers published on a yearly basis
Papers
TL;DR: In this paper, the authors consider colimits and limits in restriction categories and explore various conditions under which the coproducts are "extensive" in the sense that the total category (of the related partial map category) becomes an extensive category.
Abstract: A restriction category is an abstract formulation for a category of partial maps, defined in terms of certain specified idempotents called the restriction idempotents All categories of partial maps are restriction categories; conversely, a restriction category is a category of partial maps if and only if the restriction idempotents split Restriction categories facilitate reasoning about partial maps as they have a purely algebraic formulation
In this paper we consider colimits and limits in restriction categories As the notion of restriction category is not self-dual, we should not expect colimits and limits in restriction categories to behave in the same manner The notion of colimit in the restriction context is quite straightforward, but limits are more delicate The suitable notion of limit turns out to be a kind of lax limit, satisfying certain extra properties
Of particular interest is the behaviour of the coproduct both by itself and with respect to partial products We explore various conditions under which the coproducts are ``extensive'' in the sense that the total category (of the related partial map category) becomes an extensive category When partial limits are present, they become ordinary limits in the total category Thus, when the coproducts are extensive we obtain as the total category a lextensive category This provides, in particular, a description of the extensive completion of a distributive category
83 citations
TL;DR: Three characterizations of the category L-FTOP of L-fuzzy topological spaces and their L- fuzzy continuous mappings are presented by means of the categories L-FNS, L- FIS and L-FCS.
74 citations
1 Jan 2004
TL;DR: In this paper, the authors construct and give basic properties of a flbered coproduct in the category of ringed spaces, which is just a particular type of colimit.
Abstract: We flrst construct and give basic properties of a flbered coproduct in the category of ringed spaces (which is just a particular type of colimit). We then look at some special cases where this actually gives a flbered coproduct in the category of schemes. Intuitively this is gluing a collection of schemes along some collection of other schemes (possibly subschemes). We then use this to construct a scheme without closed points.
65 citations
TL;DR: In this paper, potato coproducts are quantitatively important energy sources in beef cattle diets, which, in turn, solve a potentially massive disposal problem for the food processing industry.
Abstract: Wet coproducts fed to beef cattle include processing coproducts of the fruit, vegetable, juice, and brewing industries. Considerations for their utilization in beef cattle diets include quantity available, feeding value, quality of animal products produced, economics (e.g., transportation of water), storage and preservation, consumer perception, nuisance concerns, contaminants, and interactions with other diet ingredients. Potato (Solanum tuberosum) coproducts from processing for frozen food products may be quantitatively most important because the 11.3 million t of potatoes (fresh weight) processed in the United States and Canada in 2008 resulted in an estimated 4.3 million t (as-is basis) of coproduct. Chemical composition and feeding value of potato coproducts depends on the coproduct type. The names of coproducts vary among potato processors and some processors combine the different coproducts into one product commonly called slurry. The 4 main potato coproducts are 1) potato peels; 2) screen solids (small potatoes and pieces); 3) fried product (fries, hash browns, batter, crumbles); and 4) material from the water recovery systems (oxidation ditch, belt solids, filter cake). The coproducts, except the fried products, ensile rapidly, reaching pH 5 in 7 d or less. Dry matter content varies from 10 to 30% and on a DM basis varies in CP (5 to 27%), starch (3 to 56%), NDF (4 to 41%), and ether extract (3 to 37%) content among potato coproducts. Type of coproduct and frying greatly affect the energy value (0.6 to 1.6 Mcal of NE(g)/kg of DM). Composition, quality, and shelf life of beef was not affected by potato coproduct feeding in contrast to perceptions of some purveyors and chefs. Potato coproducts are quantitatively important energy sources in beef cattle diets, which, in turn, solve a potentially massive disposal problem for the food processing industry.
61 citations
TL;DR: A topological construction, the “reduced coproduct”, which makes sense for indexed collections of arbitrary Tichonov spaces, is derived and it is shown how one may use this construction to gain information about the category of compact Hausdorff spaces.
Abstract: By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the “reduced coproduct”, which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the “ultracoproduct” can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems dealing with the topological structure of reduced coproducts (especially ultracoproducts) and show in addition how one may use this construction to gain information about the category of compact Hausdorff spaces.
49 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 18 |
| 2024 | 44 |
| 2023 | 45 |
| 2022 | 101 |
| 2021 | 17 |
| 2020 | 9 |